DYNNLO version Introduction

Transcription

1 DYNNLO version 1.5 This is a note about the DYNNLO program. DYNNLO is a parton level Monte Carlo program that computes the cross section for vector-boson production in pp and p p collisions. The calculation is performed up to NNLO in QCD perturbation theory. The program includes γ Z interference, finite-width effects, the leptonic decay of the vector boson and the corresponding spin correlations. The user is allowed to apply arbitrary (though infrared safe) cuts on the final state and to plot the corresponding distributions in the form of bin histograms. If you use this program, please quote Ref. [1]. 1 Introduction The DYNNLO program is based on an extension of the subtraction formalism to NNLO, as described in Ref. [1]. The calculation is organized in two parts. In the first part (virtual), the contribution of the regularized virtual corrections (up to two-loop order) is computed. In the second part (real), the cross section for the production of the vector boson in association with (at least) one jet is first evaluated up to NLO (i.e. up to O(αS 2 )). This step of the calculation can be performed with any available version of the subtraction method. Here we use the dipole formalism [3], as implemented in the MCFM Monte Carlo program [4]. Since the V + jet cross section is divergent when the transverse momentum q T of the vector boson becomes small, a suitable counterterm must be subtracted to make the result finite as q T 0. The program uses the counterterm introduced in the second paper of Ref. [1], and thus it completes the evaluation of the real part. Finally, the two contributions (virtual and real) are combined to obtain the full cross section. In the present version of the code, the evaluation of the subtraction counterterm is made substantially faster than before. The program can be downloaded from To extract it, simply use tar -xzvf dynnlo-v1.5.tgz and the dynnlo-v1.5 directory will be created. The structure of the directory is bin: The directory containing the executable dynnlo and the input and output files. doc: The directory containing this note. obj: The directory containing the object files. src: The directory containing the source of the code. 1

2 2 Input parameters In our calculation, the W and Z bosons are treated off shell, thus including finite-width effects, and their leptonic decay retains the corresponding spin correlations. The mass and total width of the W boson are m W = GeV and Γ W = GeV. The mass and total width of the Z boson are m Z = GeV and Γ Z = GeV. As for the electroweak couplings, we use the so called G µ scheme, where the input parameters are G F, m Z, m W. The Fermi constant is set to the value G F = GeV 2, and we use the following (unitarity constrained) values of the CKM matrix elements: V ud = , V us = , V ub = , V cd = , V cs = , V cb = All these values of EW parameters are taken from the PDG 2012 [2]. The EW couplings of the W and Z bosons to quarks and leptons are treated at the tree level, so that the above parameters are sufficient to fully specify the EW content of our calculation. 3 Implementation of cuts Before compiling the program, the user must choose the cuts to apply on the final state. This is done through the cuts and isolation functions. The default version of the function cuts contains selection cuts that are typically used in the experimental analysis. In the default version, the lines of the code implementing the various cuts are all commented, thus the program will return the total cross section for the selected process in the narrow width approximation. To take into account finite width effect the logical variable zerowidth should be set to false in the input file 1. To activate the various cuts the user must uncomment the corresponding lines in cuts.f. Lepton isolation can be implemented by switching to true the logical variable isol. The parameters to define the isolation procedure are set in the isolation function. The program makes possible the identification of final-state jets, in addition to the leptons. Jets [5] are reconstructed according to the k T algorithm with R = 0.4. Different jet algorithms (as the anti-k T or the cone) and different values of R can be implemented by modifying the setup subroutine. The files cuts.f and isolation.f can be found in the /src/user directory. The setup.f source file can be found in the /src/need directory. 4 Compilation The program is self-contained and it has been successfully tested on Linux and Mac-OS X environments. To compile the code, descend in the dynnlo directory and simply type make To run it go in the bin directory and type: dynnlo < infile 5 The input file This is a typical example of input file: 8d3! sroot 1 Note that with zerowidth=.false. a hard scale must be set, to have a cross section that is computable in QCD perturbation theory. The hard scale is set by applying cuts on the leptons. These cuts must necessarily enforce a lower limit on the invariant mass of the vector boson (lepton pair), and the mass scale of this lower limit must be in the perturbative region. 2

3 1 1! ih1, ih2 1! nproc d d0! mur, muf 2! order tota! part.false.! zerowidth 50d0 7d3! mwmin, mwmax ! itmx1, ncall ! itmx2, ncall2 617! rseed 92 0! set, member (native PDFs) MSTW2008lo68cl.LHgrid 0! set, member (LHAPDFs) nnlo! runstring sroot: Double precision variable for centre of mass energy (GeV). ih1,ih2: Integers identifying the beam (proton=1, antiproton=-1). nproc: Integeridentifyingtheprocess: W + l + ν (nproc=1),w l ν (nproc=2), Z/γ l + l (nproc=3). mur, muf: Renormalization (µ R ) and factorization (µ F ) scales (GeV): can be be different from each other but always of the order of m W or m Z (or m lν and m ll if these invariant masses are very different from m W and m Z ). By switching to true the logical variable dynamicscale in the setup subroutine, µ R and µ F are set equal to m lν or m ll. order: Integer setting the order of the calculation: LO (0), NLO (1), NNLO (2). part: String identifying the part of the calculation to be performed: virt for virtual contribution, real for real contribution, tota for the complete calculation. itmx1, ncall1: Number of iterations and calls to VEGAS for setting the grid. zerowidth: When this logical variable is set to true the vector bosons are produced on-shell. To take into account finite width effect this variable should be set to false. mwmin, mwmax: Lower and higher limit on the vector boson (lepton pair) invariant mass. itmx2, ncall2: Number of iterations and calls to VEGAS for the main run. rseed: Random number seed. iset, nset: Integers identifying respectively the PDF set chosen and the member for PDF errors (if the native PDF interface is used). A list of available PDFs is given below. PDFname, PDFmember: String identifying the PDF set chosen and integer identifying the member for PDF errors (if the LHAPDF interface is used). runstring: String for grid and output files. 3

4 6 Output At the end of the run, the program returns the cross section and its error. The program also writes an output file in the topdrawer format containing the required histograms with an estimate of the corresponding statistical errors. During the run, the user can control the intermediate results. The plots are defined in the file /src/user/plotter.f. The user can easily modify this subroutine according to his/her needs. The NLO computation of a cross section with accuracy at the percent level typically requires a few hours of run on a standard PC (say a Pentium 4 at 3 GHz). At NNLO the required run time is between one and two days. To obtain smooth distributions, this estimated run time should be multiplied by a factor of two. 7 Parton distributions The DYNNLO program can be compiled with its own Parton Distribution Functions (PDF) interface (set PDFROUTINES = NATIVE in the makefile) or with the LHAPDF interface (set PDFROUTINES = LHAPDF in the makefile). We point out that the value of α S (m Z ) is not adjustable; it is hard-wired with the value of α S (m Z ) in the parton distributions. Moreover, the choice of the parton distributions also specifies the number of loops that should be used in the running of α S. A list of available parton densities for the native PDF interface is given in Table 1. When dealing with PDF uncertainties, the nset variable is used to distinguish the PDF grids corresponding to different eigenvectors. When CTEQ6.6M partons are used, nset varies in the range nset=0,44. When NNPDF partons are used, nset varies in the range nset=0,100. When MSTW2008 partons are used, nset varies in the range nset=0,40 and the uncertainties we consider are those at 68% CL. When GJR08VF NLO or JR09VF NNLO partons are used, the nset variable should be in the range nset=-13,13. For A06 (ABKM09) NNLO partons, the variable nset should vary in the range nset=0,23 (nset=0,25). The default choice is nset=0, corresponding to the central set. The variable nset is dummy when other PDF sets are used. 8 From version 1.1 to version 1.2 The main change done in version 1.2 with respect to version 1.1 is that the evaluation of the subtraction counterterm is made substantially faster. As a consequence, the speed of the code improves by at least a factor 1.5. A minor bug has been corrected in the dynamic scale settings, whose effect is however negligible. 9 From version 1.2 to version 1.3 The only change done in version 1.3 with respect to version 1.2 is that a bug affecting the program when running with dynamicscale=.false. has been fixed. 10 From version 1.3 to version 1.4 In version 1.4 some refinements in the subtraction procedure have been implemented and two bugs affecting the real and the virtual contribution has been fixed. 4

5 11 From version 1.4 to version 1.5 In version 1.5 a bug in the factorization scale dependence has been corrected. References [1] S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Phys. Rev. Lett. 103 (2009) ; S. Catani and M. Grazzini, Phys. Rev. Lett. 98 (2007) [2] J. Beringer et al. [Particle Data Group Collaboration], Phys. Rev. D 86 (2012) [3] S. Catani and M. H. Seymour, Phys. Lett. B 378 (1996) 287, Nucl. Phys. B 485 (1997) 291 [Erratum-ibid. B 510 (1998) 503]. [4] J. Campbell, R.K. Ellis, MCFM - Monte Carlo for FeMtobarn processes, [5] S. Catani, Y. L. Dokshitzer, M. H. Seymour and B. R. Webber, Nucl. Phys. B 406 (1993) 187; S. D. Ellis and D. E. Soper, Phys. Rev. D 48 (1993)

6 iset Pdf set α S (M Z ) 1 CTEQ4 LO CTEQ4 Standard NLO MRST98 NLO central gluon MRST98 NLO higher gluon MRST98 NLO lower gluon MRST98 NLO lower α S MRST98 NLO higher α S MRST98 LO CTEQ5M NLO Standard Msbar CTEQ5D NLO DIS CTEQ5L LO CTEQ5HJ NLO Large-x gluon enhanced CTEQ5HQ NLO Heavy Quark CTEQ5M1 NLO Improved CTEQ5HQ1 NLO Improved MRST99 NLO MRST99 higher gluon MRST99 lower gluon MRST99 lower α S MRST99 higher α S MRST2001 NLO central gluon MRST2001 NLO lower α S MRST2001 NLO higher α S MRST2001 NLO better fit to jet data MRST2001 NNLO MRST2001 NNLO fast evolution MRST2001 NNLO slow evolution MRST2001 NNLO better fit to jet data CTEQ6L LO CTEQ6L1 LO CTEQ6M NLO CTEQ6.6M NLO MRST2002 LO MRST2002 NLO MRST2002 NNLO GJR08VF LO GJR08VF NLO JR09VF NNLO MRST2004 NLO MRST2004 NNLO A06 NNLO NNPDF NLO ABKM09 NNLO MSTW2008 LO MSTW2008 NLO MSTW2008 NNLO Table 1: Available pdf sets and their corresponding iset and values of α S (M Z ). 6